Generalized central limit theorem theory

One can also view (29) as a generalization of Cramer s LDT [62]. Recall that this theory treats the wings of a distribution like V(m) correctly, to which the central limit theorem (CLT) does not apply [63]. However, the CLT approximation in this problem has quite a beautiful interpretation and is worth describing separately. It can be derived by assuming that n (cr) is itself a Gaussian in Eq. (29), or just written down directly ... 

In general, we can say that the sum of a great number of random values is controlled by a Gaussian distribution of probabilities, like (6.16). This is one of the key ideas in probability theory. Due to its great importance, it was given a posh name, the central limit theorem (CLT). 

Much current theoretical work is devoted to finding a more fundamental and general underlying theory from which the standard model of particle physics could be deduced as the low energy limit. String theory and the inclusion of the gravitational interaction are central viewpoints, and in such theories particles may have structure and the CPT theorem may be violated. 

The Gaussian distribution is generally assumed to govern random experimental errors. The central limit theory of statistics gives some justification for this assumption. This theorem states that if a number of random variables (independent variables) xi,X2,. ..,x are all governed by probability distributions with finite means... 

---